Statistical mechanics of vortices from field theory

Nuclear Physics B

Volumn 559, Issue 1-2, 1999, Pages 395-428

  Kajantie, K ^f   Laine, M ^a   Neuhaus, T ^b,c   Rajantie, A ^d   Rummukainen, K ^e  

^a CERN   (Switzerland)

^b RWTH AACHEN UNIVERSITY   (Germany)

^c BIELEFELD UNIVERSITY   (Germany)

^d UNIVERSITY OF SUSSEX   (United Kingdom)

^e NORDITA   (Denmark)

^f NONE

Author keywords

Finite temperature; Lattice simulations; Magnetic field; Phase diagram; Vortices

Indexed keywords

EID: 0033581543     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(99)00464-2     Document Type: Article

References (49)

1. [1] J. Ranft, J. Kripfganz and G. Ranft, Phys. Rev. D 28 (1983) 360; M.N. Chernodub, M.I. Polikarpov and M.A. Zubkov, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 256,hep-lat/9401027; M. Chavel, Phys. Lett. B 378 (1996) 227, hep-lat/9603005.
2. [1] J. Ranft, J. Kripfganz and G. Ranft, Phys. Rev. D 28 (1983) 360; M.N. Chernodub, M.I. Polikarpov and M.A. Zubkov, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 256, hep-lat/9401027; M. Chavel, Phys. Lett. B 378 (1996) 227, hep-lat/9603005.
3. [1] J. Ranft, J. Kripfganz and G. Ranft, Phys. Rev. D 28 (1983) 360; M.N. Chernodub, M.I. Polikarpov and M.A. Zubkov, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 256,hep-lat/9401027; M. Chavel, Phys. Lett. B 378 (1996) 227, hep-lat/9603005.
4. [2] A. Rajantie, Physica B 255 (1998) 108, cond-mat/9803221; K. Kajantie, M. Karjalainen, M. Laine, J. Peisa and A. Rajantie, Phys. Lett. B 428 (1998) 334, hep-ph/9803367.
5. [2] A. Rajantie, Physica B 255 (1998) 108, cond-mat/9803221; K. Kajantie, M. Karjalainen, M. Laine, J. Peisa and A. Rajantie, Phys. Lett. B 428 (1998) 334, hep-ph/9803367.
6. [3] K. Kajantie, M. Laine, T. Neuhaus, J. Peisa, A. Rajantie and K. Rummukainen, Nucl. Phys. B 546 (1999) 351, hep-ph/9809334.
7. [4] G. Blatter, MV. Feigel'man, V.B. Geshkenbein, A.I. Larkin and V.M. Vinokur, Rev. Mod. Phys. 66 (1994) 1125.
8. [ 5] D.S. Fisher, M.P.A. Fisher and D.A. Huse, Phys. Rev. B 43 (1991) 130.
9. [6] R.E. Hetzel, A. Sudbø and D.A. Huse, Phys. Rev. Lett. 69 (1992) 518.
10. [7] E. Zeldov, D. Majer, M. Konczykowski, V.B. Geshkenbein, V.M. Vinokur and H. Shtrikman, Nature 375 (1995) 373; A. Schilling, R.A. Fisher, N.E. Phillips, U. Welp, D. Dasgupta, W.K. Kwok and G.W. Crabtree, Nature 382 (1996) 791.
11. [7] E. Zeldov, D. Majer, M. Konczykowski, V.B. Geshkenbein, V.M. Vinokur and H. Shtrikman, Nature 375 (1995) 373; A. Schilling, R.A. Fisher, N.E. Phillips, U. Welp, D. Dasgupta, W.K. Kwok and G.W. Crabtree, Nature 382 (1996) 791.
12. [8] P.H. Damgaard and U.M. Heller, Phys. Rev. Lett. 60 (1988) 1246; Nucl. Phys. B 309 (1988) 625.
13. [8] P.H. Damgaard and U.M. Heller, Phys. Rev. Lett. 60 (1988) 1246; Nucl. Phys. B 309 (1988) 625.
14. [9] K. Kajantie, M. Laine, J. Peisa, K. Rummukainen and M. Shaposhnikov, Nucl. Phys. B 544 (1999) 357, hep-lat/9809004.
15. [10] K. Farakos, G. Koutsoumbas and N.E. Mavromatos, Phys. Lett. B 431 (1998) 147, hep-lat/9802037.
16. [11] K. Farakos, K. Kajantie, K. Rummukainen and M. Shaposhnikov, Nucl. Phys. B 425 (1994) 67, hep-ph/9404201.
17. [12] K. Kajantie, M. Karjalainen, M. Laine and J. Peisa, Phys. Rev. B 57 (1998) 3011, cond-mat/9704056; Nucl. Phys. B 520 (1998) 345, hep-lat/9711048.
18. [12] K. Kajantie, M. Karjalainen, M. Laine and J. Peisa, Phys. Rev. B 57 (1998) 3011, cond-mat/9704056; Nucl. Phys. B 520 (1998) 345, hep-lat/9711048.
19. [13] J.O. Andersen, Phys. Rev. D 59 (1999) 065015.
20. [14] H. Kleinert, Gauge Fields in Condensed Matter (World Scientific, Singapore, 1989).
21. [15] E.M. Lifshitz and L.P. Pitaevskii, Statistical Physics, Part 2, §45 (Pergamon Press, Oxford, 1980).
22. [16] M. Laine and A. Rajantie, Nucl. Phys. B 513 (1998) 471, hep-lat/9705003.
23. [17] G.D. Moore, Nucl. Phys. B 493 (1997) 439, hep-lat/9610013; Nucl. Phys. B 523 (1998) 569, hep-lat/9709053.
24. [17] G.D. Moore, Nucl. Phys. B 493 (1997) 439, hep-lat/9610013; Nucl. Phys. B 523 (1998) 569, hep-lat/9709053.
25. [18] L. Jacobs and C. Rebbi, Phys. Rev. B 19 (1979) 4486.
26. [19] P.A. Shah and N.S. Manton, J. Math. Phys. 35 (1994) 1171, hep-th/9307165; N.S. Manton and S.M. Nasir, hep-th/9809071.
27. [19] P.A. Shah and N.S. Manton, J. Math. Phys. 35 (1994) 1171, hep-th/9307165; N.S. Manton and S.M. Nasir, hep-th/9809071.
28. [20] J.C. Osborn and A.T. Dorsey, Phys. Rev. B 50 (1994) 15961, cond-mat/9411015;
29. A.T. Dorsey, Ann. Phys. 233 ( 1994) 248.
30. [21] E.V. Thuneberg, Phys. Rev. B 44 (1991) 9685.
31. [22] L.M.A. Bettencourt and R.J. Rivers, Phys. Rev. D 51 (1995) 1842, hep-ph/9405222.
32. [23] B.I. Halperin, T.C. Lubensky and S.-K. Ma, Phys. Rev. Lett. 32 (1974) 292; C. Dasgupta and B.I. Halperin, Phys. Rev. Lett. 47 (1981) 1556; J. Bartholomew, Phys. Rev. B 28 (1983) 5378; Y. Munehisa, Phys. Lett. B 155 (1985) 159; P. Dimopoulos, K. Farakos and G. Kotsoumbas, Eur. Phys. J. C 1 (1998) 711, hep-lat/9703004.
33. [23] B.I. Halperin, T.C. Lubensky and S.-K. Ma, Phys. Rev. Lett. 32 (1974) 292; C. Dasgupta and B.I. Halperin, Phys. Rev. Lett. 47 (1981) 1556; J. Bartholomew, Phys. Rev. B 28 (1983) 5378; Y. Munehisa, Phys. Lett. B 155 (1985) 159; P. Dimopoulos, K. Farakos and G. Kotsoumbas, Eur. Phys. J. C 1 (1998) 711, hep-lat/9703004.
34. [23] B.I. Halperin, T.C. Lubensky and S.-K. Ma, Phys. Rev. Lett. 32 (1974) 292; C. Dasgupta and B.I. Halperin, Phys. Rev. Lett. 47 (1981) 1556; J. Bartholomew, Phys. Rev. B 28 (1983) 5378; Y. Munehisa, Phys. Lett. B 155 (1985) 159; P. Dimopoulos, K. Farakos and G. Kotsoumbas, Eur. Phys. J. C 1 (1998) 711, hep-lat/9703004.
35. [23] B.I. Halperin, T.C. Lubensky and S.-K. Ma, Phys. Rev. Lett. 32 (1974) 292; C. Dasgupta and B.I. Halperin, Phys. Rev. Lett. 47 (1981) 1556; J. Bartholomew, Phys. Rev. B 28 (1983) 5378; Y. Munehisa, Phys. Lett. B 155 (1985) 159; P. Dimopoulos, K. Farakos and G. Kotsoumbas, Eur. Phys. J. C 1 (1998) 711, hep-lat/9703004.
36. [23] B.I. Halperin, T.C. Lubensky and S.-K. Ma, Phys. Rev. Lett. 32 (1974) 292; C. Dasgupta and B.I. Halperin, Phys. Rev. Lett. 47 (1981) 1556; J. Bartholomew, Phys. Rev. B 28 (1983) 5378; Y. Munehisa, Phys. Lett. B 155 (1985) 159; P. Dimopoulos, K. Farakos and G. Kotsoumbas, Eur. Phys. J. C 1 (1998) 711, hep-lat/9703004.
37. [24] K. Kajantie, M. Laine, K. Rummukainen and M. Shaposhnikov, Nucl. Phys. B 493 (1997) 413, hep-lat/9612006; A. Hart, O. Philipsen, J.D. Stack and M. Teper, Phys. Lett. B 396 (1997) 217, hep-lat/9612021; K. Rummukainen, M. Tsypin, K. Kajantie, M. Laine and M. Shaposhnikov, Nucl. Phys. B 532 (1998)283, hep-lat/9805013; K. Kajantie, M. Laine, A. Rajantie, K. Rummukainen and M. Tsypin, JHEP 11 (1998) 011, hep-lat/9811004.
38. [24] K. Kajantie, M. Laine, K. Rummukainen and M. Shaposhnikov, Nucl. Phys. B 493 (1997) 413, hep-lat/9612006; A. Hart, O. Philipsen, J.D. Stack and M. Teper, Phys. Lett. B 396 (1997) 217, hep-lat/9612021; K. Rummukainen, M. Tsypin, K. Kajantie, M. Laine and M. Shaposhnikov, Nucl. Phys. B 532 (1998)283, hep-lat/9805013; K. Kajantie, M. Laine, A. Rajantie, K. Rummukainen and M. Tsypin, JHEP 11 (1998) 011, hep-lat/9811004.
39. [24] K. Kajantie, M. Laine, K. Rummukainen and M. Shaposhnikov, Nucl. Phys. B 493 (1997) 413, hep-lat/9612006; A. Hart, O. Philipsen, J.D. Stack and M. Teper, Phys. Lett. B 396 (1997) 217, hep-lat/9612021; K. Rummukainen, M. Tsypin, K. Kajantie, M. Laine and M. Shaposhnikov, Nucl. Phys. B 532 (1998) 283, hep-lat/9805013; K. Kajantie, M. Laine, A. Rajantie, K. Rummukainen and M. Tsypin, JHEP 11 (1998) 011, hep-lat/9811004.
40. [24] K. Kajantie, M. Laine, K. Rummukainen and M. Shaposhnikov, Nucl. Phys. B 493 (1997) 413, hep-lat/9612006; A. Hart, O. Philipsen, J.D. Stack and M. Teper, Phys. Lett. B 396 (1997) 217, hep-lat/9612021; K. Rummukainen, M. Tsypin, K. Kajantie, M. Laine and M. Shaposhnikov, Nucl. Phys. B 532 (1998)283, hep-lat/9805013; K. Kajantie, M. Laine, A. Rajantie, K. Rummukainen and M. Tsypin, JHEP 11 (1998) 011, hep-lat/9811004.
41. [25] Z. Tešanović, Phys. Rev. B 51 (1995) 16204; Phys. Rev. B 59 (1999) 6449, cond-mat/9801306; A.K. Kienappel and M.A. Moore, cond-mat/9705151; cond-mat/9809317; A.K. Nguyen and A. Sudbø, Europhys. Lett. 46 (1999) 780, cond-mat/9811149; cond-mat/9907385.
42. [25] Z. Tešanović, Phys. Rev. B 51 (1995) 16204; Phys. Rev. B 59 (1999) 6449, cond-mat/9801306; A.K. Kienappel and M.A. Moore, cond-mat/9705151; cond-mat/9809317; A.K. Nguyen and A. Sudbø, Europhys. Lett. 46 (1999) 780, cond-mat/9811149; cond-mat/9907385.
43. [25] Z. Tešanović, Phys. Rev. B 51 (1995) 16204; Phys. Rev. B 59 (1999) 6449, cond-mat/9801306; A.K. Kienappel and M.A. Moore, cond-mat/9705151; cond-mat/9809317; A.K. Nguyen and A. Sudbø, Europhys. Lett. 46 (1999) 780, cond-mat/9811149; cond-mat/9907385.
44. [25] Z. Tešanović, Phys. Rev. B 51 (1995) 16204; Phys. Rev. B 59 (1999) 6449, cond-mat/9801306; A.K. Kienappel and M.A. Moore, cond-mat/9705151; cond-mat/9809317; A.K. Nguyen and A. Sudbø, Europhys. Lett. 46 (1999) 780, cond-mat/9811149; cond-mat/9907385.
45. [26] M. Karjalainen and J. Peisa, Z. Phys. C 76 (1997) 319, hep-lat/9607023.
46. [27] J. Ambjørn and P. Olesen, Nucl. Phys. B 315 (1989) 606; Phys. Lett. B 218 (1989) 67; Nucl. Phys. B330 (1990) 193; Int. J. Mod. Phys. A 5 (1990) 4525.
47. [27] J. Ambjørn and P. Olesen, Nucl. Phys. B 315 (1989) 606; Phys. Lett. B 218 (1989) 67; Nucl. Phys. B330 (1990) 193; Int. J. Mod. Phys. A 5 (1990) 4525.
48. [27] J. Ambjørn and P. Olesen, Nucl. Phys. B 315 (1989) 606; Phys. Lett. B 218 (1989) 67; Nucl. Phys. B 330 (1990) 193; Int. J. Mod. Phys. A 5 (1990) 4525.
49. [27] J. Ambjørn and P. Olesen, Nucl. Phys. B 315 (1989) 606; Phys. Lett. B 218 (1989) 67; Nucl. Phys. B330 (1990) 193; Int. J. Mod. Phys. A 5 (1990) 4525.